Anatomy of $B\rightarrow D\bar{D}$ Decays

TL;DR

This paper analyzes $B ightarrow Dar{D}$ decays to understand CP violation and non-perturbative effects, using current data and symmetry principles to improve the precision of mixing phase measurements.

Contribution

It provides a comprehensive analysis of $B ightarrow Dar{D}$ decays, constraining non-perturbative parameters and testing factorisation, with implications for future CP violation measurements.

Findings

Evidence for enhanced exchange and penguin annihilation topologies.

Indications of potentially enhanced penguin contributions.

Patterns in branching ratios suggest significant non-factorisable effects.

Abstract

The decays $B_d^0\rightarrow D_d^-D_d^+$ and $B_s^0\rightarrow D_s^-D_s^+$ probe the CP-violating mixing phases $\phi_d$ and $\phi_s$, respectively. The theoretical uncertainty of the corresponding determinations is limited by contributions from penguin topologies, which can be included with the help of the $U$-spin symmetry of the strong interaction. We analyse the currently available data for $B^0_{d,s}\rightarrow D_{d,s}^-D_{d,s}^+$ decays and those with similar dynamics to constrain the involved non-perturbative parameters. Using further information from semileptonic $B_d^0\rightarrow D_d^-\ell^+\nu_{\ell}$ decays, we perform a test of the factorisation approximation and take non-factorisable $SU(3)$-breaking corrections into account. The branching ratios of the $B_d^0\rightarrow D_d^-D_d^+$, $B_s^0\rightarrow D_s^-D_d^+$ and $B_s^0\rightarrow D_s^-D_s^+$, $B_d^0\rightarrow D_d^-D_s^+$ decays show an interesting pattern which can be accommodated through significantly enhanced exchange and penguin annihilation topologies. This feature is also supported by data for the $B_s^0\rightarrow D_d^-D_d^+$ channel. Moreover, there are indications of potentially enhanced penguin contributions in the $B_d^0\rightarrow D_d^-D_d^+$ and $B_s^0\rightarrow D_s^-D_s^+$ decays, which would make it mandatory to control these effects in the future measurements of $\phi_d$ and $\phi_s$. We discuss scenarios for high-precision measurements in the era of Belle II and the LHCb upgrade.